International Journal of Quantum Information

Fundamental quantum gates can be implemented effectively using adiabatic quantum computation or circuit model. Recently, Hen combined the two approaches to introduce a new model called controlled adiabatic evolutions [I. Hen, Phys. Rev. A, 91(2) (2015) 022309]. This model was specifically designed to implement one and two-qubit controlled gates. Later, Santos extended Hen’s work to implement $n$-qubit controlled gates [A. C. Santos and M. S. Sarandy, Sci. Rep., 5 (2015) 15775]. In this paper, we discuss the implementation of each of the usual quantum gates, as well as demonstrate the possibility of preparing Bell’s states using the controlled adiabatic evolutions approach. We conclude by presenting the fidelity results of implementing single quantum gates and Bell’s states in open systems.

A symmetric informationally complete positive operator-valued measure (SIC-POVM) is a POVM in ${ℂ}^K$ consisting of $K^2$ positive operators of rank one such that all of whose Hermite inner products are equal. SIC-POVMs are important in quantum information theory, which have many applications in quantum state tomography, quantum cryptography and basic research in quantum mechanics. However, it is very difficult to construct SIC-POVMs. Therefore, many scholars have focused on approximately symmetric informationally complete positive operator-valued measures (ASIC-POVMs) for which the Hermite inner products are close to equal. In this paper, two new constructions of ASIC-POVMs are provided by using character sums and some special functions over finite fields.

When constructing quantum codes under the entanglement-assisted (EA) stabilizer formalism, one can ignore the limitation of dual-containing condition. This allows us to construct EA quantum error-correcting codes (QECCs) from any classical linear codes. The main contribution of this manuscript is to make a general statement for determining the optimal number of pre-shared qubits instead of presenting only specific cases. Let $n=\frac{q-1}{2a}(q+1)$ and $\text{gcd}(n,q)=1$, where $q$ is an odd prime power, $2a|(q-1)$ and $a\ge 3$. By deeply investigating the decomposition of the defining set of negacyclic codes, we generalize the number of pre-shared entanglement pairs of Construction (1) in Lu et al. [Quantom Inf. Process. 17 (2018) 69] from $c=2,4$ to arbitrary even numbers less than or equal to $2a$. Consequently, a series of EA quantum maximum distance separable (EAQMDS) codes can be produced. The absolute majority of them are new and the minimum distance can be up to $q+\frac{q-1}{2a}$. Moreover, this method can be applied to construct many other families of EAQECCs with good parameters, especially large minimum distance.

In this paper, we study behavior of the correlations, both quantum and classical, under adiabatic demagnetization process in systems of nuclear spins with dipole–dipole interactions in an external magnetic field and in the temperature range including positive and negative temperatures. For a two-spin system, analytical expressions for the quantum and classical correlations are obtained. It is revealed that the field dependences of the quantum and classical correlations at positive and negative temperatures are substantially different. This difference most clearly appears in the case of zero magnetic field: at negative temperature, the measures of quantum correlations tend to the maximum values with a temperature increase. At positive temperature, these quantities tend to zero at a decrease of magnetic field. It is also found that, for the nearest-neighboring spins in the same field, the values of concurrence and discord are larger at negative temperatures than at positive ones.

Semiquantum cryptography has drawn much attention in recent years since it simplifies the implementation of quantum cryptographic protocols. In this paper, we study semiquantum secure direct communication (SQSDC). Based on single-photons, we propose a two-step SQSDC protocol with identity authentication, which can be used to prevent impersonation and the man-in-the-middle attack. Different from previous protocols based on quantum entanglement or quantum memory, our protocol removes there restrictions for simplifying its physical implementation. We prove that our two-step SQSDC protocol is completely robust. That is, any adversarial attempting to learn some information on the secure message or identity strings will inevitably induce some errors that can be detected by communicators.

It was recently emphasized by Byrnes, Forster and Tessler [Phys. Rev. Lett. 120 (2018) 060501] that the continuous-time formulation of Grover’s quantum search algorithm can be intuitively understood in terms of Rabi oscillations between the source and the target subspaces. In this work, motivated by this insightful remark and starting from the consideration of a time-independent generalized quantum search Hamiltonian as originally introduced by Bae and Kwon [Phys. Rev. A 66 (2002) 012314], we present a detailed investigation concerning the physical connection between quantum search Hamiltonians and exactly solvable time-dependent two-level quantum systems. Specifically, we compute in an exact analytical manner the transition probabilities from a source state to a target state in a number of physical scenarios specified by a spin-$1∕2$ particle immersed in an external time-dependent magnetic field. In particular, we analyze both the periodic oscillatory as well as the monotonic temporal behaviors of such transition probabilities and, moreover, explore their analogy with characteristic features of Grover-like and fixed-point quantum search algorithms, respectively. Finally, we discuss from a physics standpoint the connection between the schedule of a search algorithm, in both adiabatic and nonadiabatic quantum mechanical evolutions, and the control fields in a time-dependent driving Hamiltonian.

Recently, He proposed a novel quantum private comparison protocol without a third party (G. P. He, Int. J. Quantum Inf. 15(2) (2016) 1750014). This paper points out that two security loopholes in He’s protocol are existent. And a new QPC protocol which can avoid these loopholes is proposed without the help of a third party in this paper.

A multi-party quantum summation with a single $d$-level quantum system is proposed, in which a semi-honest third party (TP) is employed. Only sequential communication of a single quantum $d$-level system (for any prime $d$) is required in the presented protocol, resulting in advantages in scalability. In addition, it can be realized with state-of-the-art technology. Due to the semi-honest TP, the protocol is not only secure against outside attacks, but also secure against participant attacks.

The classical and quantum correlations for a family of two-qutrit states are investigated. For this purpose, a family of two-qutrit states, as well as a set of measurements are proposed. An analytical quantum discord treatment is presented for this family of two-qutrit states. Finally, we compute and illustrate the entanglement of formation, classical mutual information and quantum discord for this family of two-qutrit quantum states.